Question

The value of m, if the points (5,1) (-2,-3), and (8,2m) are collinear is:

• A. $\frac{15}{14}$
• B. $\frac{19}{14}$
• C. $\frac{19}{15}$
• D. $\frac{19}{17}$

Answer 1

The correct option is B

$\frac{19}{14}$

Let A = $(x_1,y_1)$ = (5,1)
B = $(x_2,y_2)$ = (-2,-3)
C = $(x_3,y_3)$ = (8,2m)
Since, the points A = (5,1), B = (-2,-3), and C = (8,2m) are collinear.
$\therefore Areaof\Delta ABC=0\Rightarrow \frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]=0\Rightarrow \frac{1}{2}\left[5\right(-3-2m)+(-2\left)\right(2m-1)+8(1-(-3)\left)\right]=0\Rightarrow \frac{1}{2}(-15-10m-4m+2+32)=0\Rightarrow \frac{1}{2}(-14m+19)=0\Rightarrow m=\frac{19}{14}$
Hence, the required value of m is $\frac{19}{14}$.